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  Subjects -> ENGINEERING (Total: 2169 journals)
    - CHEMICAL ENGINEERING (186 journals)
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    - ENGINEERING (1176 journals)
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ENGINEERING (1176 journals)            First | 4 5 6 7 8 9 10 11 | Last

Journal of Industrial and Production Engineering     Hybrid Journal   (Followers: 3)
Journal of Industrial Engineering and Management     Open Access   (Followers: 4)
Journal of Inequalities and Applications     Open Access  
Journal of Infrared, Millimeter and Terahertz Waves     Hybrid Journal   (Followers: 1)
Journal of Integrated Design and Process Science     Hybrid Journal   (Followers: 1)
Journal of Intelligent and Fuzzy Systems     Hybrid Journal   (Followers: 9)
Journal of Inverse and Ill-posed Problems     Hybrid Journal   (Followers: 1)
Journal of Irrigation and Drainage Engineering     Full-text available via subscription   (Followers: 15)
Journal of K-Theory     Full-text available via subscription   (Followers: 1)
Journal of King Saud University - Engineering Sciences     Open Access  
Journal of Konbin     Open Access  
Journal of Liquid Chromatography & Related Technologies     Hybrid Journal   (Followers: 9)
Journal of Management in Engineering     Full-text available via subscription   (Followers: 10)
Journal of Manufacturing Science and Engineering     Full-text available via subscription   (Followers: 11)
Journal of Manufacturing Systems     Full-text available via subscription   (Followers: 6)
Journal of Manufacturing Technology Management     Hybrid Journal   (Followers: 4)
Journal of Mathematical Modelling and Algorithms     Hybrid Journal   (Followers: 2)
Journal of Mechatronics     Full-text available via subscription  
Journal of Membrane and Separation Technology     Hybrid Journal  
Journal of Metallurgy     Open Access   (Followers: 2)
Journal of Middle European Construction and Design of Cars     Open Access   (Followers: 1)
Journal of Molecular Catalysis B: Enzymatic     Hybrid Journal   (Followers: 1)
Journal of Motor Behavior     Hybrid Journal   (Followers: 9)
Journal of Multivariate Analysis     Hybrid Journal   (Followers: 6)
Journal of Nanoengineering and Nanomanufacturing     Full-text available via subscription   (Followers: 1)
Journal of Nanoparticle Research     Hybrid Journal   (Followers: 3)
Journal of Nanoscience     Open Access  
Journal of Nanoscience and Nanotechnology     Full-text available via subscription   (Followers: 12)
Journal of NanoScience, NanoEngineering & Applications     Full-text available via subscription  
Journal of Nanotechnology     Open Access   (Followers: 2)
Journal of Nanotechnology in Engineering and Medicine     Full-text available via subscription   (Followers: 6)
Journal of Natural Gas Science and Engineering     Hybrid Journal   (Followers: 3)
Journal of Near Infrared Spectroscopy     Full-text available via subscription   (Followers: 7)
Journal of Networks     Open Access   (Followers: 4)
Journal of Nonlinear Dynamics     Open Access  
Journal of Nuclear Engineering & Technology     Full-text available via subscription  
Journal of Ocean Engineering and Marine Energy     Hybrid Journal  
Journal of Oceanography and Marine Science     Open Access   (Followers: 2)
Journal of Operations Management     Hybrid Journal   (Followers: 19)
Journal of Optics     Hybrid Journal   (Followers: 2)
Journal of Optimization     Open Access  
Journal of Optoelectronics Engineering     Open Access  
Journal of Organizational Behavior     Hybrid Journal   (Followers: 32)
Journal of Petroleum Science Research     Open Access   (Followers: 1)
Journal of Phase Equilibria and Diffusion     Hybrid Journal   (Followers: 5)
Journal of Power Sources     Partially Free   (Followers: 30)
Journal of Pre-College Engineering Education Research     Open Access  
Journal of Pressure Vessel Technology     Full-text available via subscription   (Followers: 11)
Journal of Professional Issues in Engineering Education and Practice     Full-text available via subscription   (Followers: 6)
Journal of Quality and Reliability Engineering     Open Access   (Followers: 1)
Journal of Quality in Maintenance Engineering     Hybrid Journal   (Followers: 4)
Journal of Radiation Research and Applied Sciences     Open Access   (Followers: 1)
Journal of Rare Earths     Full-text available via subscription   (Followers: 2)
Journal of Real-Time Image Processing     Hybrid Journal   (Followers: 6)
Journal of Regional Science     Hybrid Journal   (Followers: 10)
Journal of Reinforced Plastics and Composites     Hybrid Journal   (Followers: 24)
Journal of Research of NIST     Open Access   (Followers: 1)
Journal of Research Updates in Polymer Science     Hybrid Journal  
Journal of Rock Mechanics and Geotechnical Engineering     Open Access   (Followers: 2)
Journal of Russian Laser Research     Hybrid Journal  
Journal of Safety Engineering     Open Access   (Followers: 5)
Journal of Safety Research     Hybrid Journal   (Followers: 19)
Journal of Science and Technology     Open Access  
Journal of Science and Technology (Ghana)     Open Access   (Followers: 2)
Journal of Science and Technology Policy Management     Hybrid Journal   (Followers: 2)
Journal of Scientific Computing     Hybrid Journal   (Followers: 3)
Journal of Scientific Innovations for Development     Open Access   (Followers: 2)
Journal of Semiconductors     Full-text available via subscription   (Followers: 2)
Journal of Sensor Technology     Open Access   (Followers: 3)
Journal of Shanghai Jiaotong University (Science)     Hybrid Journal  
Journal of Sol-Gel Science and Technology     Hybrid Journal   (Followers: 2)
Journal of Solar Energy     Open Access   (Followers: 5)
Journal of Solar Energy Engineering     Full-text available via subscription   (Followers: 16)
Journal of Superconductivity and Novel Magnetism     Partially Free   (Followers: 1)
Journal of Surface Investigation. X-ray, Synchrotron and Neutron Techniques     Hybrid Journal   (Followers: 1)
Journal of Surveying Engineering     Full-text available via subscription   (Followers: 7)
Journal of Technology Management & Innovation     Open Access   (Followers: 3)
Journal of Telecommunications Management     Full-text available via subscription   (Followers: 3)
Journal of Testing and Evaluation     Full-text available via subscription   (Followers: 11)
Journal of the Air & Waste Management Association     Hybrid Journal   (Followers: 3)
Journal of the Chinese Institute of Engineers     Hybrid Journal  
Journal of the Chinese Institute of Industrial Engineers     Hybrid Journal   (Followers: 1)
Journal of the Franklin Institute     Full-text available via subscription   (Followers: 2)
Journal of the Institution of Engineers (India ): Series D     Hybrid Journal  
Journal of the Institution of Engineers (India) : Series B     Hybrid Journal   (Followers: 1)
Journal of The Institution of Engineers (India) : Series E     Hybrid Journal   (Followers: 1)
Journal of the Institution of Engineers (India): Series A     Hybrid Journal  
Journal of the Institution of Engineers (India): Series C     Hybrid Journal   (Followers: 1)
Journal of the National Science Foundation of Sri Lanka     Open Access   (Followers: 1)
Journal of the University of Ruhuna     Open Access  
Journal of Thermal Science and Engineering Applications     Full-text available via subscription   (Followers: 3)
Journal of Thermal Stresses     Hybrid Journal   (Followers: 3)
Journal of Transplantation     Open Access   (Followers: 3)
Journal of Transport and Supply Chain Management     Open Access   (Followers: 6)
Journal of Transportation Engineering     Full-text available via subscription   (Followers: 14)
Journal of Transportation Systems Engineering and Information Technology     Full-text available via subscription   (Followers: 15)
Journal of Tribology     Full-text available via subscription   (Followers: 28)
Journal of Turbomachinery     Full-text available via subscription   (Followers: 10)
Journal of Turbulence     Hybrid Journal  
Journal of Unmanned Vehicle Systems     Full-text available via subscription   (Followers: 2)

  First | 4 5 6 7 8 9 10 11 | Last

Journal Cover   Physica D: Nonlinear Phenomena
  [SJR: 1.048]   [H-I: 89]   [3 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0167-2789
   Published by Elsevier Homepage  [2812 journals]
  • Mobile localized solutions for an electron in lattices with dispersive and
           non-dispersive phonons
    • Abstract: Publication date: Available online 27 May 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Luis A. Cisneros-Ake , Leonor Cruzeiro , Manuel G. Velarde
      We consider a one dimensional lattice in which an electron can interact both with on-site non-dispersive (Einstein) phonons and with longitudinal dispersive acoustic (Debye) phonons. We provide existence conditions for mobile localized electron excitations in the long wave limit. The role of both types of phonon modes on localization is also assessed, together with a discussion of differences existing between the discrete and the continuum approaches. A striking result is that, under certain conditions, localized states can only be stable if they have a non-zero velocity.


      PubDate: 2015-05-28T15:34:49Z
       
  • Synchronization of finite-state pulse-coupled oscillators
    • Abstract: Publication date: 15 May 2015
      Source:Physica D: Nonlinear Phenomena, Volume 303
      Author(s): Hanbaek Lyu
      We propose a novel generalized cellular automaton (GCA) model for discrete-time pulse-coupled oscillators and study the emergence of synchrony. Given a finite simple graph and an integer n ≥ 3 , each vertex is an identical oscillator of period n with the following weak coupling along the edges: each oscillator inhibits its phase update if it has at least one neighboring oscillator at a particular ”blinking” state and if its state is ahead of this blinking state. We obtain conditions on initial configurations and on network topologies for which states of all vertices eventually synchronize. We show that our GCA model synchronizes arbitrary initial configurations on paths, trees, and with random perturbation, any connected graph. In particular, our main result is the following local–global principle for tree networks: for n ∈ { 3 , 4 , 5 , 6 } , any n -periodic network on a tree synchronizes arbitrary initial configuration if and only if the maximum degree of the tree is less than the period n .


      PubDate: 2015-05-23T16:37:48Z
       
  • Wave amplification in the framework of forced nonlinear Schrödinger
           equation: The rogue wave context
    • Abstract: Publication date: 15 May 2015
      Source:Physica D: Nonlinear Phenomena, Volume 303
      Author(s): Alexey Slunyaev , Anna Sergeeva , Efim Pelinovsky
      Irregular waves which experience the time-limited external forcing within the framework of the nonlinear Schrödinger (NLS) equation are studied numerically. It is shown that the adiabatically slow pumping (the time scale of forcing is much longer than the nonlinear time scale) results in selective enhancement of the solitary part of the wave ensemble. The slow forcing provides eventually wider wavenumber spectra, larger values of kurtosis and higher probability of large waves. In the opposite case of rapid forcing the nonlinear waves readjust passing through the stage of fast surges of statistical characteristics. Single forced envelope solitons are considered with the purpose to better identify the role of coherent wave groups. An approximate description on the basis of solutions of the integrable NLS equation is provided. Applicability of the Benjamin–Feir Index to forecasting of conditions favourable for rogue waves is discussed.


      PubDate: 2015-05-23T16:37:48Z
       
  • Editorial Board
    • Abstract: Publication date: 15 May 2015
      Source:Physica D: Nonlinear Phenomena, Volume 303




      PubDate: 2015-05-23T16:37:48Z
       
  • Signal amplification factor in stochastic resonance: An analytic
           non-perturbative approach
    • Abstract: Publication date: 15 May 2015
      Source:Physica D: Nonlinear Phenomena, Volume 303
      Author(s): Asish Kumar Dhara
      The response of an overdamped bistable system driven by a Gaussian white noise and perturbed by a weak monochromatic force (signal) is studied analytically. In order to get amplitude-dependent signal amplification factor a non-perturbative scheme is put forward by taking into account all the terms of a perturbation series with amplitude of the signal as an expansion parameter. An approximate analytic expression of the signal amplification factor is derived and compared with the numerical results. The contributions of infinite number of relaxation modes of the stochastic dynamics to the response are also taken into account in the final expression. The calculation of the response based on the derived expression requires only the knowledge of the first non-trivial eigenvalue and the lowest eigenfunction of the unperturbed Fokker–Planck operator.


      PubDate: 2015-05-23T16:37:48Z
       
  • Multistability and hidden attractors in a relay system with hysteresis
    • Abstract: Publication date: Available online 19 May 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Zhanybai T. Zhusubaliyev , Erik Mosekilde , Vasily G. Rubanov , Roman A. Nabokov
      For nonlinear dynamic systems with switching control, the concept of a “hidden attractor” naturally applies to a stable dynamic state that either (1) coexists with the stable switching cycle or (2), if the switching cycle is unstable, has a basin of attraction that doesn’t intersect with the neighborhood of that cycle. We show how the equilibrium point of a relay system disappears in a boundary-equilibrium bifurcation as the system enters the region of autonomous switching dynamics and demonstrate experimentally how a relay system can exhibit large amplitude chaotic oscillations at high values of the supply voltage. By investigating a four-dimensional model of the experimental relay system we finally show how a variety of hidden periodic, quasiperiodic and chaotic attractors arise, transform and disappear through different bifurcations.


      PubDate: 2015-05-23T16:37:48Z
       
  • Bifurcations and strange nonchaotic attractors in a phase oscillator model
           of glacial–interglacial cycles
    • Abstract: Publication date: Available online 22 May 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Takahito Mitsui , Michel Crucifix , Kazuyuki Aihara
      Glacial–interglacial cycles are large variations in continental ice mass and greenhouse gases, which have dominated climate variability over the Quaternary. The dominant periodicity of the cycles is ∼ 40 kyr before the so-called middle Pleistocene transition between ∼ 1.2 and ∼ 0.7 Myr ago, and it is ∼ 100 kyr after the transition. In this paper, the dynamics of glacial–interglacial cycles are investigated using a phase oscillator model forced by the time-varying incoming solar radiation (insolation). We analyze the bifurcations of the system and show that strange nonchaotic attractors appear through nonsmooth saddle-node bifurcations of tori. The bifurcation analysis indicates that mode-locking is likely to occur for the 41 kyr glacial cycles but not likely for the 100 kyr glacial cycles. The sequence of mode-locked 41 kyr cycles are robust to small parameter changes. However, the sequence of 100 kyr glacial cycles can be sensitive to parameter changes when the system has a strange nonchaotic attractor.


      PubDate: 2015-05-23T16:37:48Z
       
  • Editorial Board
    • Abstract: Publication date: 1 March 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 295–296




      PubDate: 2015-05-23T16:37:48Z
       
  • Barriers to transport and mixing in volume-preserving maps with nonzero
           flux
    • Abstract: Publication date: 1 March 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 295–296
      Author(s): Adam M. Fox , Rafael de la Llave
      We identify some geometric structures (secondary tori) that restrict transport and prevent mixing in perturbations of integrable volume-preserving systems with nonzero net flux. Unlike the customary KAM tori, secondary tori cannot be continued to the tori present in the integrable system but are generated by resonances and have a contractible direction. We also note that secondary tori persist under the addition of a net flux, which destroys all customary KAM tori. We introduce a remarkably simple algorithm to analyze the behavior of volume preserving maps and to obtain quantitative properties of the secondary tori. We then implement the algorithm and, after running it, present assertions regarding the distribution of the escape times of the unbounded orbits, the abundance of secondary tori, the size of the resonant regions, and the robustness of the tori under the addition of a mean flux.


      PubDate: 2015-05-23T16:37:48Z
       
  • Pitchfork–Hopf bifurcations in 1D neural field models with
           transmission delays
    • Abstract: Publication date: 15 March 2015
      Source:Physica D: Nonlinear Phenomena, Volume 297
      Author(s): K. Dijkstra , S.A. van Gils , S.G. Janssens , Yu.A. Kuznetsov , S. Visser
      Recently, local bifurcation theory for delayed neural fields was developed. In this paper, we show how symmetry arguments and residue calculus can be used to simplify the computation of the spectrum in special cases and the evaluation of the normal form coefficients, respectively. This is done hand in hand with an extensive study of two pitchfork–Hopf bifurcations for a 1D neural field model with ‘Wizard hat’ type connectivity.


      PubDate: 2015-05-23T16:37:48Z
       
  • Direct dynamical energy cascade in the modified KdV equation
    • Abstract: Publication date: 15 March 2015
      Source:Physica D: Nonlinear Phenomena, Volume 297
      Author(s): Denys Dutykh , Elena Tobisch
      In this study we examine the energy transfer mechanism during the nonlinear stage of the Modulational Instability (MI) in the modified Korteweg–de Vries (mKdV) equation. The particularity of this study consists in considering the problem essentially in the Fourier space. A dynamical energy cascade model of this process originally proposed for the focusing NLS-type equations is transposed to the mKdV setting using the existing connections between the KdV-type and NLS-type equations. The main predictions of the D -cascade model are outlined and validated by direct numerical simulations of the mKdV equation using the pseudo-spectral methods. The nonlinear stages of the MI evolution are also investigated for the mKdV equation.


      PubDate: 2015-05-23T16:37:48Z
       
  • Complex short pulse and coupled complex short pulse equations
    • Abstract: Publication date: 15 March 2015
      Source:Physica D: Nonlinear Phenomena, Volume 297
      Author(s): Bao-Feng Feng
      In the present paper, we propose a complex short pulse equation and a coupled complex short equation to describe ultra-short pulse propagation in optical fibers. They are integrable due to the existence of Lax pairs and infinite number of conservation laws. Furthermore, we find their multi-soliton solutions in terms of pfaffians by virtue of Hirota’s bilinear method. One- and two-soliton solutions are investigated in details, showing favorable properties in modeling ultra-short pulses with a few optical cycles. Especially, same as the coupled nonlinear Schrödinger equation, there is an interesting phenomenon of energy redistribution in soliton interactions. It is expected that, for the ultra-short pulses, the complex and coupled complex short pulses equation will play the same roles as the nonlinear Schrödinger equation and coupled nonlinear Schrödinger equation.


      PubDate: 2015-05-23T16:37:48Z
       
  • Editorial Board
    • Abstract: Publication date: 15 March 2015
      Source:Physica D: Nonlinear Phenomena, Volume 297




      PubDate: 2015-05-23T16:37:48Z
       
  • The long time behavior of Brownian motion in tilted periodic potentials
    • Abstract: Publication date: 15 March 2015
      Source:Physica D: Nonlinear Phenomena, Volume 297
      Author(s): Liang Cheng , Nung Kwan Yip
      A variety of phenomena in physics and other fields can be modeled as Brownian motion in a heat bath under tilted periodic potentials. We are interested in the long time average velocity considered as a function of the external force, that is, the tilt of the potential. In many cases, the long time behavior–pinning and de-pinning phenomenon–has been observed. We use the method of stochastic differential equation to study the Langevin equation describing such diffusion. In the over-damped limit, we show the convergence of the long time average velocity to that of the Smoluchowski–Kramers approximation, and carry out asymptotic analysis based on Risken’s and Reimann et al.’s formula. In the under-damped limit, applying Freidlin et al.’s theory, we first show the existence of three pinning and de-pinning thresholds of the normalized tilt, corresponding to the bi-stability phenomenon; and second, as noise approaches zero, derive formulas of the mean transition times between the pinning and running states.


      PubDate: 2015-05-23T16:37:48Z
       
  • Long range annealing of defects in germanium by low energy plasma ions
    • Abstract: Publication date: 15 March 2015
      Source:Physica D: Nonlinear Phenomena, Volume 297
      Author(s): J.F.R. Archilla , S.M.M. Coelho , F.D. Auret , V.I. Dubinko , V. Hizhnyakov
      Ions arriving at a semiconductor surface with very low energy (2–8 eV) are interacting with defects deep inside the semiconductor. Several different defects were removed or modified in Sb-doped germanium, of which the E -center has the highest concentration. The low fluence and low energy of the plasma ions imply that the energy has to be able to travel in a localized way to be able to interact with defects up to a few microns below the semiconductor surface. After eliminating other possibilities (electric field, light, heat) we now conclude that moving intrinsic localized modes (ILMs), as a mechanism of long-distance energy transport, are the most likely cause. This would be striking evidence of the importance of ILMs in crystals and opens the way to further experiments to probe ILM properties both in semiconductors and in the metals used for contacts. Although most of the measurements have been performed on germanium, similar effects have been found in silicon.


      PubDate: 2015-05-23T16:37:48Z
       
  • O(2) Hopf bifurcation of viscous shock waves in a channel
    • Abstract: Publication date: Available online 1 April 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Alin Pogan , Jinghua Yao , Kevin Zumbrun
      Extending work of Texier and Zumbrun in the semilinear non-reflection symmetric case, we study O ( 2 ) transverse Hopf bifurcation, or “cellular instability”, of viscous shock waves in a channel, for a class of quasilinear hyperbolic–parabolic systems including the equations of thermoviscoelasticity. The main difficulties are to (i) obtain Fréchet differentiability of the time- T solution operator by appropriate hyperbolic–parabolic energy estimates, and (ii) handle O ( 2 ) symmetry in the absence of either center manifold reduction (due to lack of spectral gap) or (due to nonstandard quasilinear hyperbolic-parabolic form) the requisite framework for treatment by spatial dynamics on the space of time-periodic functions, the two standard treatments for this problem. The latter issue is resolved by Lyapunov–Schmidt reduction of the time- T map, yielding a four-dimensional problem with O ( 2 ) plus approximate S 1 symmetry, which we treat “by hand” using direct Implicit Function Theorem arguments. The former is treated by balancing information obtained in Lagrangian coordinates with that from associated constraints. Interestingly, this argument does not apply to gas dynamics or magnetohydrodynamics (MHD), due to the infinite-dimensional family of Lagrangian symmetries corresponding to invariance under arbitrary volume-preserving diffeomorphisms.


      PubDate: 2015-05-23T16:37:48Z
       
  • A renormalization approach to the universality of scaling in phyllotaxis
    • Abstract: Publication date: 1 April 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 298–299
      Author(s): Christian H. Reick
      Phyllotaxis, i.e. the arrangement of plant organs like leaves, florets, scales, bracts etc. around a shoot, stem, or cone, is often highly regular. Across the plant kingdom phyllotaxis shows not only qualitatively, but also quantitatively identical features, like the occurrence of divergence angles close to noble irrationals. In a previous study (Reick, 2012) a mechanism has been identified that explains the selection of these particular divergence angles on the basis of self-similarity and scaling, numerically found in the bifurcation diagrams of simple dynamical models of phyllataxis. In the present paper, by constructing a renormalization theory, the universality of this scaling is proved for a whole class of models, prototypically represented by Thornley’s model of phyllotaxis (Thornley, 1975). The renormalization is constructed from another self-similarity found numerically for the Fourier transform of the abstract potential governing the mutual inhibition of primordia. Surprisingly, the resulting renormalization transformation is already known from the treatment of the quasiperiodic transition to chaos but operates here on a different function space. It turns out that the fixed points of the renormalization transformation are characterized by divergences of the form Θ ( κ ) = 1 / τ ( κ ) , where, written as continued fraction, τ ( κ ) = [ κ ; κ , κ , … ] , κ ∈ N + . To show the universality of the scaling, it is demonstrated that the fixed points are unstable and that the associated scaling factors α ( κ ) = − ( τ ( κ ) ) 2 and β ( κ ) = τ ( κ ) are exactly those that were numerically found in (Reick, 2012) to rule the selfsimilarity of the bifurcation structure. Thereby, the present paper puts forward an explanation for the universal appearance of certain phyllotactic patterns that is independent of physiological detail of plant growth.


      PubDate: 2015-05-23T16:37:48Z
       
  • Groove growth by surface subdiffusion
    • Abstract: Publication date: 1 April 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 298–299
      Author(s): M. Abu Hamed , A.A. Nepomnyashchy
      The investigation of the grain-boundary groove growth by normal surface diffusion was first done by Mullins. However, the diffusion on a solid surface is often anomalous. Recently, the groove growth in the case of surface superdiffusion has been analyzed. In the present paper, the problem of the groove growth is solved in the case of the surface subdiffusion. An exact self-similar solution is obtained and represented in terms of the Fox H-function. Basic properties of the solution are described.


      PubDate: 2015-05-23T16:37:48Z
       
  • Tracking pattern evolution through extended center manifold reduction and
           singular perturbations
    • Abstract: Publication date: 1 April 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 298–299
      Author(s): L. Sewalt , A. Doelman , H.G.E. Meijer , V. Rottschäfer , A. Zagaris
      In this paper we develop an extended center manifold reduction method: a methodology to analyze the formation and bifurcations of small-amplitude patterns in certain classes of multi-component, singularly perturbed systems of partial differential equations. We specifically consider systems with a spatially homogeneous state whose stability spectrum partitions into eigenvalue groups with distinct asymptotic properties. One group of successive eigenvalues in the bifurcating group are widely interspaced, while the eigenvalues in the other are stable and cluster asymptotically close to the origin along the stable semi-axis. The classical center manifold reduction provides a rigorous framework to analyze destabilizations of the trivial state, as long as there is a spectral gap of sufficient width. When the bifurcating eigenvalue becomes commensurate to the stable eigenvalues clustering close to the origin, the center manifold reduction breaks down. Moreover, it cannot capture subsequent bifurcations of the bifurcating pattern. Through our methodology, we formally derive expressions for low-dimensional manifolds exponentially attracting the full flow for parameter combinations that go beyond those allowed for the (classical) center manifold reduction, i.e. to cases in which the spectral gap condition no longer can be satisfied. Our method also provides an explicit description of the flow on these manifolds and thus provides an analytical tool to study subsequent bifurcations. Our analysis centers around primary bifurcations of transcritical type–that can be either of co-dimension 1 or 2–in two- and three-component PDE systems. We employ our method to study bifurcation scenarios of small-amplitude patterns and the possible appearance of low-dimensional spatio-temporal chaos. We also exemplify our analysis by a number of characteristic reaction–diffusion systems with disparate diffusivities.


      PubDate: 2015-05-23T16:37:48Z
       
  • On extreme events for non-spatial and spatial branching Brownian motions
    • Abstract: Publication date: 1 April 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 298–299
      Author(s): Jean Avan , Nicolas Grosjean , Thierry Huillet
      We study the impact of having a non-spatial branching mechanism with infinite variance on some parameters (height, width and first hitting time) of an underlying Bienaymé–Galton–Watson branching process. Aiming at providing a comparative study of the spread of an epidemics whose dynamics is given by the modulus of a branching Brownian motion (BBM) we then consider spatial branching processes in dimension d , not necessarily integer. The underlying branching mechanism is either a binary branching model or one presenting infinite variance. In particular we evaluate the chance p ( x ) of being hit if the epidemics started away at distance x . We compute the large x tail probabilities of this event, both when the branching mechanism is regular and when it exhibits very large fluctuations.


      PubDate: 2015-05-23T16:37:48Z
       
  • Blended particle methods with adaptive subspaces for filtering turbulent
           dynamical systems
    • Abstract: Publication date: 1 April 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 298–299
      Author(s): Di Qi , Andrew J. Majda
      It is a major challenge throughout science and engineering to improve uncertain model predictions by utilizing noisy data sets from nature. Hybrid methods combining the advantages of traditional particle filters and the Kalman filter offer a promising direction for filtering or data assimilation in high dimensional turbulent dynamical systems. In this paper, blended particle filtering methods that exploit the physical structure of turbulent dynamical systems are developed. Non-Gaussian features of the dynamical system are captured adaptively in an evolving-in-time low dimensional subspace through particle methods, while at the same time statistics in the remaining portion of the phase space are amended by conditional Gaussian mixtures interacting with the particles. The importance of both using the adaptively evolving subspace and introducing conditional Gaussian statistics in the orthogonal part is illustrated here by simple examples. For practical implementation of the algorithms, finding the most probable distributions that characterize the statistics in the phase space as well as effective resampling strategies is discussed to handle realizability and stability issues. To test the performance of the blended algorithms, the forty dimensional Lorenz 96 system is utilized with a five dimensional subspace to run particles. The filters are tested extensively in various turbulent regimes with distinct statistics and with changing observation time frequency and both dense and sparse spatial observations. In real applications perfect dynamical models are always inaccessible considering the complexities in both modeling and computation of high dimensional turbulent system. The effects of model errors from imperfect modeling of the systems are also checked for these methods. The blended methods show uniformly high skill in both capturing non-Gaussian statistics and achieving accurate filtering results in various dynamical regimes with and without model errors.


      PubDate: 2015-05-23T16:37:48Z
       
  • Editorial Board
    • Abstract: Publication date: 1 April 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 298–299




      PubDate: 2015-05-23T16:37:48Z
       
  • Arithmetic exponents in piecewise-affine planar maps
    • Abstract: Publication date: 1 April 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 298–299
      Author(s): John A.G. Roberts , Franco Vivaldi
      We consider the growth of some indicators of arithmetical complexity of rational orbits of (piecewise) affine maps of the plane, with rational parameters. The exponential growth rates are expressed by a set of exponents; one exponent describes the growth rate of the so-called logarithmic height of the points of an orbit, while the others describe the growth rate of the size of such points, measured with respect to the p -adic metric. Here p is any prime number which divides the parameters of the map. We show that almost all the points in a domain of linearity (such as an elliptic island in an area-preserving map) have the same set of exponents. We also show that the convergence of the p -adic exponents may be non-uniform, with arbitrarily large fluctuations occurring arbitrarily close to any point. We explore numerically the behaviour of these quantities in the chaotic regions, in both area-preserving and dissipative systems. In the former case, we conjecture that wherever the Lyapunov exponent is zero, the arithmetical exponents achieve a local maximum.


      PubDate: 2015-05-23T16:37:48Z
       
  • Effects of interactions on the dynamics of driven cold atoms
    • Abstract: Publication date: 15 April 2015
      Source:Physica D: Nonlinear Phenomena, Volume 300
      Author(s): Alexandra Bakman , Shmuel Fishman
      The quantum fidelity was introduced by Peres to study some fingerprints of classically chaotic behavior in the quantum dynamics of the corresponding systems. In the present paper the signatures of classical dynamics near elliptic points and of interactions between particles are characterized for kicked systems. In particular, the period of the fidelity resulting of the interactions is found using analytical and numerical calculations. A mechanism leading to the oscillations with the intermediate period is proposed. It is of a classical origin and results of the interplay between the oscillations of the width of the wave packets and the rotation of their center around the elliptic fixed point.


      PubDate: 2015-05-23T16:37:48Z
       
  • Modulational instabilities of periodic traveling waves in deep water
    • Abstract: Publication date: 15 April 2015
      Source:Physica D: Nonlinear Phenomena, Volume 300
      Author(s): Benjamin F. Akers
      The spectrum of periodic traveling waves in deep water is discussed. A multi-scale method is used, expanding the spectral data and the Bloch parameter in wave amplitude, to compute the size and location of modulated instabilities. The role of these instabilities in limiting the spectrum’s analyticity is explained. Both two-dimensional and three-dimensional instabilities are calculated. The asymptotic predictions are compared to numerical simulations.


      PubDate: 2015-05-23T16:37:48Z
       
  • (Non)Uniqueness of critical points in variational data assimilation
    • Abstract: Publication date: 15 April 2015
      Source:Physica D: Nonlinear Phenomena, Volume 300
      Author(s): Graham Cox
      In this paper we apply the 4D-Var data assimilation scheme to the initialization problem for a family of quasilinear evolution equations. The resulting variational problem is non-convex, so it need not have a unique minimizer. We comment on the implications of non-uniqueness for numerical applications, then prove uniqueness results in the following situations: (1) the observational times are sufficiently small; (2) the prior covariance is sufficiently small. We also give an example of a data set where the cost functional has a critical point of arbitrarily large Morse index, thus demonstrating that the geometry can be highly nonconvex even for a relatively mild nonlinearity.


      PubDate: 2015-05-23T16:37:48Z
       
  • Considerations on conserved quantities and boundary conditions of the
           2+1-dimensional nonlinear Schrödinger equation
    • Abstract: Publication date: 15 April 2015
      Source:Physica D: Nonlinear Phenomena, Volume 300
      Author(s): Javier Villarroel , Julia Prada
      In this study, we consider a natural integrable generalization of the defocusing cubic nonlinear Schrödinger equation to two dimensions and we classify the admissible boundary conditions. In particular, we determine whether the classical physical observables are conserved: mass, momentum, and Hamiltonian. We find that this is the case when a certain integral (the mass constraint) vanishes. The vanishing of the mass constraint, and thus the existence of conserved quantities, is contingent on the boundary conditions adopted. In particular, under decaying boundary conditions, the Hamiltonian is not necessarily conserved.


      PubDate: 2015-05-23T16:37:48Z
       
  • Editorial Board
    • Abstract: Publication date: 15 April 2015
      Source:Physica D: Nonlinear Phenomena, Volume 300




      PubDate: 2015-05-23T16:37:48Z
       
  • Kadomtsev–Petviashvili II equation: Structure of asymptotic soliton
           webs
    • Abstract: Publication date: 15 April 2015
      Source:Physica D: Nonlinear Phenomena, Volume 300
      Author(s): Shai Horowitz , Yair Zarmi
      A wealth of observations, recently supported by rigorous analysis, indicate that, asymptotically in time, most multi-soliton solutions of the Kadomtsev–Petviashvili II equation self-organize in webs comprised of solitons and soliton-junctions. Junctions are connected in pairs, each pair—by a single soliton. The webs expand in time. As distances between junctions grow, the memory of the structure of junctions in a connected pair ceases to affect the structure of either junction. As a result, every junction propagates at a constant velocity, which is determined by the wave numbers that go into its construction. One immediate consequence of this characteristic is that asymptotic webs preserve their morphology as they expand in time. Another consequence, based on simple geometric considerations, explains why, except in special cases, only 3-junctions (“ Y -shaped”, involving three wave numbers) and 4-junctions (“ X -shaped”, involving four wave numbers) can partake in the construction of an asymptotic soliton web.


      PubDate: 2015-05-23T16:37:48Z
       
  • Derivation of a wave kinetic equation from the resonant-averaged
           stochastic NLS equation
    • Abstract: Publication date: Available online 22 April 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Sergei Kuksin , Alberto Maiocchi
      We suggest a new derivation of a wave kinetic equation for the spectrum of the weakly nonlinear Schrödinger equation with stochastic forcing. The kinetic equation is obtained as a result of a double limiting procedure. Firstly, we consider the equation on a finite box with periodic boundary conditions and send the size of the nonlinearity and of the forcing to zero, while the time is correspondingly rescaled; then, the size of the box is sent to infinity (with a suitable rescaling of the solution). We report here the results of the first limiting procedure, analysed with full rigour in Kuksin and Maiocchi (0000), and show how the second limit leads to a kinetic equation for the spectrum, if some further hypotheses (commonly employed in the weak turbulence theory) are accepted. Finally we show how to derive from these equations the Kolmogorov-Zakharov spectra.


      PubDate: 2015-05-23T16:37:48Z
       
  • Elliptical optical solitary waves in a finite nematic liquid crystal cell
    • Abstract: Publication date: 1 May 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 301–302
      Author(s): Antonmaria A. Minzoni , Luke W. Sciberras , Noel F. Smyth , Annette L. Worthy
      The addition of orbital angular momentum has been previously shown to stabilise beams of elliptic cross-section. In this article the evolution of such elliptical beams is explored through the use of an approximate methodology based on modulation theory. An approximate method is used as the equations that govern the optical system have no known exact solitary wave solution. This study brings to light two distinct phases in the evolution of a beam carrying orbital angular momentum. The two phases are determined by the shedding of radiation in the form of mass loss and angular momentum loss. The first phase is dominated by the shedding of angular momentum loss through spiral waves. The second phase is dominated by diffractive radiation loss which drives the elliptical solitary wave to a steady state. In addition to modulation theory, the “chirp” variational method is also used to study this evolution. Due to the significant role radiation loss plays in the evolution of an elliptical solitary wave, an attempt is made to couple radiation loss to the chirp variational method. This attempt furthers understanding as to why radiation loss cannot be coupled to the chirp method. The basic reason for this is that there is no consistent manner to match the chirp trial function to the generated radiating waves which is uniformly valid in time. Finally, full numerical solutions of the governing equations are compared with solutions obtained using the various variational approximations, with the best agreement achieved with modulation theory due to its ability to include both mass and angular momentum losses to shed diffractive radiation.


      PubDate: 2015-05-23T16:37:48Z
       
  • The nonlinear interaction of convection modes in a box of a saturated
           porous medium
    • Abstract: Publication date: 1 May 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 301–302
      Author(s): Brendan J. Florio , Andrew P. Bassom , Neville Fowkes , Kevin Judd , Thomas Stemler
      A plethora of convection modes may occur within a confined box of porous medium when the associated dimensionless Rayleigh number R is above some critical value dependent on the geometry. In many cases the crucial Rayleigh number R c for onset is different for each mode, and in practice the mode with the lowest associated R c is likely to be the dominant one. For particular sizes of box, however, it is possible for multiple modes (typically three) to share a common R c . For box shapes close to these special geometries the modes interact and compete nonlinearly near the onset of convection. Here this mechanism is explored and it is shown that generically the dynamics of the competition takes on one of two possible structures. A specific example of each is described, while the general properties of the system enables us to compare our results with some previous calculations for particular box dimensions.


      PubDate: 2015-05-23T16:37:48Z
       
  • Controlling synchrony in a network of Kuramoto oscillators with
           time-varying coupling
    • Abstract: Publication date: 1 May 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 301–302
      Author(s): Rachel Leander , Suzanne Lenhart , Vladimir Protopopescu
      The Kuramoto model describes the synchronization of a heterogeneous population of oscillators through a stationary homogeneous network in which oscillators are coupled via their phase differences. Recently, there has been interest in studying synchronization on time-varying networks, and time-varying generalizations of the Kuramoto network, in particular. Previous results indicate that networks with fast dynamics may be as efficient as static networks at promoting synchrony. In this paper we use optimal control theory to study synchronization on a time-varying Kuramoto network. Our results indicate that time-varying networks can be more efficient than static networks at promoting synchrony and show that fast network dynamics are not necessary for efficiency. In particular, we show that, near the synchronization threshold, time-varying networks can promote synchrony through slow oscillations that lengthen the duration of high synchrony states and shorten the duration of low synchrony states. Interestingly, repulsion is an essential feature of these optimal dynamic networks.


      PubDate: 2015-05-23T16:37:48Z
       
  • Exchange orbits in the planar 1+4 body problem
    • Abstract: Publication date: 1 May 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 301–302
      Author(s): A. Bengochea , J. Galán , E. Pérez-Chavela
      We study some doubly-symmetric orbits in the planar 1 + 2 n -body problem, that is the mass of the central body is significantly bigger than the other 2 n equal masses. The necessary and sufficient conditions for periodicity of the orbits are discussed. We also study numerically these kinds of orbits for the case n = 2 . The system under study corresponds to one conformed by a planet and four satellites of equal mass. We determine a 1 -parameter family of time-reversible invariant tori, related with the reversing symmetries of the equations of motion. The initial conditions of the orbits were determined by means of solving a boundary value problem with one free parameter. The numerical solution of the boundary value problem was obtained using the software AUTO. For the numerical analysis we have used the value of 3.5 × 1 0 − 4 as mass ratio of some satellite and the planet. In the computed solutions the satellites are in mean motion resonance 1:1 and they librate around a relative equilibria, that is a solution where the distances between the bodies remain constant for all time.


      PubDate: 2015-05-23T16:37:48Z
       
  • Editorial Board
    • Abstract: Publication date: 1 May 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 301–302




      PubDate: 2015-05-23T16:37:48Z
       
  • Hamiltonian formulation of the extended Green–Naghdi equations
    • Abstract: Publication date: 1 May 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 301–302
      Author(s): Yoshimasa Matsuno
      A novel method is developed for extending the Green–Naghdi (GN) shallow-water model equation to the general system which incorporates the arbitrary higher-order dispersive effects. As an illustrative example, we derive a model equation which is accurate to the fourth power of the shallowness parameter while preserving the full nonlinearity of the GN equation, and obtain its solitary wave solutions by means of a singular perturbation analysis. We show that the extended GN equations have the same Hamiltonian structure as that of the GN equation. We also demonstrate that Zakharov’s Hamiltonian formulation of surface gravity waves is equivalent to that of the extended GN system by rewriting the former system in terms of the momentum density instead of the velocity potential at the free surface.


      PubDate: 2015-05-23T16:37:48Z
       
  • Nonlinear propagating localized modes in a 2D hexagonal crystal lattice
    • Abstract: Publication date: 1 May 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 301–302
      Author(s): Janis Bajars , J. Chris Eilbeck , Benedict Leimkuhler
      In this paper we consider a 2D hexagonal crystal lattice model first proposed by Marín, Eilbeck and Russell in 1998. We perform a detailed numerical study of nonlinear propagating localized modes, that is, propagating discrete breathers and kinks. The original model is extended to allow for arbitrary atomic interactions, and to allow atoms to travel out of the unit cell. A new on-site potential is considered with a periodic smooth function with hexagonal symmetry. We are able to confirm the existence of long-lived propagating discrete breathers. Our simulations show that, as they evolve, breathers appear to localize in frequency space, i.e. the energy moves from sidebands to a main frequency band. Our numerical findings shed light on the open question of whether exact moving breather solutions exist in 2D hexagonal layers in physical crystal lattices.


      PubDate: 2015-05-23T16:37:48Z
       
  • Blow up Criterion of strong solution for 3D viscous liquid-gas two-phase
           flow model with vacuum
    • Abstract: Publication date: Available online 5 May 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Lili Du , Qin Zhang
      In this paper, we construct a blow-up criterion of the local strong solution to the three-dimensional (3D) viscous liquid-gas two-phase flow model only in terms of the divergence of the velocity field. Moreover, the initial vacuum is allowed, and there is no extra restriction on viscous coefficients. Both the Cauchy problem and initial–boundary value problem are considered in this paper.


      PubDate: 2015-05-23T16:37:48Z
       
  • Numerical study of blow-up and dispersive shocks in solutions to
           generalized Korteweg-de Vries equations
    • Abstract: Publication date: Available online 4 May 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): C. Klein , R. Peter
      We present a detailed numerical study of solutions to general Korteweg-de Vries equations with critical and supercritical nonlinearity, both in the context of dispersive shocks and blow-up. We study the stability of solitons and show that they are unstable against being radiated away and blow-up. In the L 2 critical case, the blow-up mechanism by Martel, Merle and Raphaël can be numerically identified. In the limit of small dispersion, it is shown that a dispersive shock always appears before an eventual blow-up. In the latter case, always the first soliton to appear will blow up. It is shown that the same type of blow-up as for the perturbations of the soliton can be observed which indicates that the theory by Martel, Merle and Raphaël is also applicable to initial data with a mass much larger than the soliton mass. We study the scaling of the blow-up time t ∗ in dependence of the small dispersion parameter ϵ and find an exponential dependence t ∗ ( ϵ ) and that there is a minimal blow-up time t 0 ∗ greater than the critical time of the corresponding Hopf solution for ϵ → 0 . To study the cases with blow-up in detail, we apply the first dynamic rescaling for generalized Korteweg-de Vries equations. This allows to identify the type of the singularity.


      PubDate: 2015-05-23T16:37:48Z
       
  • Partial classification of Lorenz knots: Syllable permutations of torus
           knots words
    • Abstract: Publication date: Available online 12 May 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Paulo Gomes , Nuno Franco , Luís Silva
      We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston’s theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.


      PubDate: 2015-05-23T16:37:48Z
       
  • Phyllotaxis: Some progress, but a story far from over
    • Abstract: Publication date: Available online 15 May 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Matthew F. Pennybacker , Patrick D. Shipman , Alan C. Newell
      This is a review article with a point of view. We summarize the long history of the subject and recent advances and suggest that almost all features of the architecture of shoot apical meristems can be captured by pattern-forming systems which model the biochemistry and biophysics of those regions on plants.


      PubDate: 2015-05-23T16:37:48Z
       
  • Synchronization of coupled chaotic maps
    • Abstract: Publication date: Available online 12 May 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Georgi S. Medvedev , Xuezhi Tang
      We prove a sufficient condition for synchronization for coupled one-dimensional maps and estimate the size of the window of parameters where synchronization takes place. It is shown that coupled systems on graphs with positive eigenvalues of the normalized graph Laplacian concentrated around 1 are more amenable for synchronization. In the light of this condition, we review spectral properties of Cayley, quasirandom, power–law graphs, and expanders and relate them to synchronization of the corresponding networks. The analysis of synchronization on these graphs is illustrated with numerical experiments. The results of this paper highlight the advantages of random connectivity for synchronization of coupled chaotic dynamical systems.


      PubDate: 2015-05-23T16:37:48Z
       
  • Continuous data assimilation for the 2D Bénard convection through
           velocity measurements alone
    • Abstract: Publication date: 15 May 2015
      Source:Physica D: Nonlinear Phenomena, Volume 303
      Author(s): Aseel Farhat , Michael S. Jolly , Edriss S. Titi
      An algorithm for continuous data assimilation for the two-dimensional Bénard convection problem is introduced and analyzed. It is inspired by the data assimilation algorithm developed for the Navier–Stokes equations, which allows for the implementation of variety of observables: low Fourier modes, nodal values, finite volume averages, and finite elements. The novelty here is that the observed data is obtained for the velocity field alone; i.e. no temperature measurements are needed for this algorithm. We provide conditions on the spatial resolution of the observed data, under the assumption that the observed data is free of noise, which are sufficient to show that the solution of the algorithm approaches, at an exponential rate, the unique exact unknown solution of the Bénard convection problem associated with the observed (finite dimensional projection of) velocity.


      PubDate: 2015-05-23T16:37:48Z
       
  • Canalization and the Stability of NK–Kauffman Networks
    • Abstract: Publication date: Available online 15 May 2015
      Source:Physica D: Nonlinear Phenomena
      Author(s): Federico Zertuche
      Boolean variables are such that they take values on Z 2 ≅ { 0 , 1 } . NK–Kauffman networks are dynamical deterministic systems of N Boolean functions that depend only on K ≤ N Boolean variables. They were proposed by Kauffman as a first step to understand cellular behavior (Kauffman, 1969) with great success. Among the problems that still have not been well understood in Kauffman networks, is the mechanism that regulates the phase transition of the system from an ordered phase where small changes of the initial state decay; to a chaotic one, where they grow exponentially. I show, that this mechanism is regulated through the irreducible decomposition of Boolean functions proposed in Zertuche (2009). This is in contrast to previous knowledge that attributed it to canalization. I also review other statistical properties of Kauffman networks that Boolean irreducibility explains.


      PubDate: 2015-05-23T16:37:48Z
       
  • Transitions between symmetric and nonsymmetric regimes in binary-mixture
           convection
    • Abstract: Publication date: 15 May 2015
      Source:Physica D: Nonlinear Phenomena, Volume 303
      Author(s): Esteban Meca , Isabel Mercader , Laureano Ramírez-Piscina
      We present here a comprehensive picture of the different bifurcations found for small to moderate Rayleigh number in binary-mixture convection with lateral heating and negative separation ratio ( S ). The present work connects the symmetric regime found for pure fluid ( S = 0 ) (Mercader et al., 2005) with the fundamentally nonsymmetric regime found for S = − 1 (Meca et al., 2004) [2,3]. We give a global context as well as an interpretation for the different associations of bifurcations found, and in particular we interpret an association of codimension-two bifurcations in terms of a higher codimension bifurcation never found, to our knowledge, in the study of an extended system.


      PubDate: 2015-05-23T16:37:48Z
       
  • The Russo–Smereka kinetic equation: Conservation laws, reductions
           and numerical solutions
    • Abstract: Publication date: 15 May 2015
      Source:Physica D: Nonlinear Phenomena, Volume 303
      Author(s): Alexander A. Chesnokov , Maxim V. Pavlov
      The one-dimension Russo–Smereka kinetic equation describing the propagation of nonlinear concentration waves in a rarefied bubbly fluid is considered. Stability of the bubbly flow in terms of hyperbolicity of the kinetic equation is studied. It is proved that a hydrodynamical chain associated with the Russo–Smereka kinetic equation possesses infinitely many conservation laws. Reductions of the model to finite component systems are derived. Conservative form of the kinetic model is proposed and numerical solution of the Cauchy problem with discontinuous initial data is obtained.


      PubDate: 2015-05-23T16:37:48Z
       
  • Self-organized populations interacting under pursuit-evasion dynamics
    • Abstract: Publication date: 1 June 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 304–305
      Author(s): Thierry Goudon , Boniface Nkonga , Michel Rascle , Magali Ribot
      We discuss the modeling of interacting populations through pursuit-evasion–or attraction–repulsion–principles : preys try to escape chasers, chasers are attracted by the presence of preys. We construct a hierarchy of models, ranging from ODEs systems with finite numbers of individuals of each population, to hydrodynamic systems. First-order macroscopic models look like generalized “two-species Keller–Segel equations”. But, due to cross-interactions, we can show that the system does not exhibit any blow up phenomena in finite time. We also obtain second-order models, that have the form of systems of balance laws, derived from kinetic models. We bring out a few remarkable features of the models based either on mathematical analysis or numerical simulations.


      PubDate: 2015-05-23T16:37:48Z
       
  • Numerical study of the generalised Klein–Gordon equations
    • Abstract: Publication date: 1 June 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 304–305
      Author(s): Denys Dutykh , Marx Chhay , Didier Clamond
      In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalised Klein–Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and multi-symplectic structures. Periodic travelling wave solutions are constructed numerically to high accuracy and compared to a seventh-order Stokes expansion of the full Euler equations. Then, we propose an efficient pseudo-spectral discretisation, which allows to assess the stability of travelling waves and localised wave packets.


      PubDate: 2015-05-23T16:37:48Z
       
  • Dynamics of erbium-doped fibre ring laser under cavity-loss modulation
    • Abstract: Publication date: 1 June 2015
      Source:Physica D: Nonlinear Phenomena, Volumes 304–305
      Author(s): Gyanendra Kumar , R. Vijaya
      The time-domain response of an erbium doped fibre laser constructed with a uni-directional ring cavity is studied when the cavity loss is sinusoidally modulated in the frequency range of the relaxation oscillation frequency of the laser. Fourier transformed data are used to analyse the spectral features. The experimental demonstration of different periodic states and chaos thus reached under the period-doubling route at kHz frequencies are substantiated with numerical calculations using parameters appropriate to the experimental conditions. Bifurcation diagrams and reconstructed attractors are calculated to show the change of different dynamical regimes while varying the modulation frequency. The modulation of intra-cavity losses in a fibre laser enables the study of its nonlinear dynamical response in a highly controlled manner.


      PubDate: 2015-05-23T16:37:48Z
       
  • Data-driven non-Markovian closure models
    • Abstract: Publication date: Available online 23 December 2014
      Source:Physica D: Nonlinear Phenomena
      Author(s): Dmitri Kondrashov , Mickaël D. Chekroun , Michael Ghil
      This paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensional system; and (ii) comparing these closure models with the optimal closures predicted by the Mori-Zwanzig (MZ) formalism of statistical physics. Multilayer stochastic models (MSMs) are introduced as both a very broad generalization and a time-continuos limit of existing multilevel, regression-based approaches to closure in a data-driven setting; these approaches include empirical model reduction (EMR), as well as more recent multi-layer modeling. It is shown that the multilayer structure of MSMs can provide a natural Markov approximation to the generalized Langevin equation (GLE) of the MZ formalism. A simple correlation-based stopping criterion for an EMR-MSM model is derived to assess how well it approximates the GLE solution. Sufficient conditions are derived on the structure of the nonlinear cross-interactions between the constitutive layers of a given MSM to guarantee the existence of a global random attractor. This existence ensures that no blow-up can occur for a very broad class of MSM applications, a class that includes non-polynomial predictors and nonlinearities that do not necessarily preserve quadratic energy invariants. The EMR-MSM methodology is applied to a conceptual, nonlinear, stochastic climate model of coupled slow and fast variables, in which only slow variables are observed. It is shown that the resulting closure model with energy-conserving nonlinearities efficiently captures the main statistical features of the slow variables, even when there is no formal scale separation and the fast variables are quite energetic. Second, an MSM is shown to successfully reproduce the statistics of a partially observed, generalized Lokta-Volterra model of population dynamics in its chaotic regime. The challenges here include the rarity of strange attractors in the model’s parameter space and the existence of multiple attractor basins with fractal boundaries. The positivity constraint on the solutions’ components replaces here the quadratic-energy–preserving constraint of fluid-flow problems and it successfully prevents blow-up.


      PubDate: 2014-12-25T15:33:57Z
       
 
 
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